Normal Versus Gamma Distribution

Safety stock (SS) is based on:

• Forecast error
• Service level target

The forecast error is modeled by using a gamma distribution:

• Gamma can be asymmetric or symmetric.
• If symmetric, a normal distribution can be used.

Service level target can be expressed using:

• Non-stockout probability
• Fill rate

Using the gamma distribution, the forecast error is modeled. If the gamma function is symmetric, a normal distribution can be used.

When comparing a Gamma distribution and a normal distribution, the Gamma distribution is more robust than the normal distribution.

The following figure shows an example of computing safety stock with a gamma distribution. Observe the following:

• Planning for one product, or one location, or one period, with instantaneous lead time.

• Forecast: 100 ± 25, forecast error distribution: gamma.

• Service Level Target: 95% non-stockout probability.

• Calculating the right safety stock requires the numerical integration of the gamma cumulative distribution function.

• Target Inventory Position = 145 units, Safety Stock = 45 units

The filled area represents 95% of total. On the stock axis, you can distinguish cycle stock and safety stock.